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A DFT Study of Electron-Phonon Coupling in
Proxy CuX (X = S, Se, Te) Structures and Its Relationship
to Possible Manifestation of Superconductivity
Paul M. Grant W2AGZ Technologies
Robert H. Hammond
Stanford University
Session Q11 Chalcogenide Superconductors
2:30 PM – 4:54 PM, Wednesday, 4 March
Paper 11 4:06 PM – 4:18 PM
Room 007B
– Our Computational Tool Box –
• DFT + Hubbard U
– Quantum Espresso
• Fermiologies, States (DOS), Phonons, e-p “Lambda”
• Graphics
– Xcrysden, XMGRACE
• Fermi Surfaces, Projected DOS
• Modeling
– Debye Temperatures a la Gibbs2 Package
• Thanks to Alberto Otero-de-la-Rosa, http://azufre.quimica.uniovi.es/src/gibbs2/gibbs2.pdf
– Then Superconductivity via Eliashberg/McMillan!
“Configuration/Coordination Space”
Relative Ground
State Energies
Tennorite
The Various Flavors of Copper “Monoxide”
“1-2-3”
tet-rs-CuO
• Siemons, et al. (2009) • Grant (2008) • Franchini Group (2011) • Cococcioni Group (2011)
Can we compute/synthesize the S, Se, Te analogues ...and what would be their physical properties wrt magnetism and superconductivity?
Magnetic properties revealed at APS MM Denver 2014. Now superconductivity!
CuO
Ground State Energies via Gibbs2: CuO & CuS
CuS
Min GSE at a0 = 4.13 Å
(Cubic)
Cubic
CuO (Cubic)
D = 693 K
Min GSE at a0 = 3.9 Å, c/a = 1.15
Tetragonal
CuO (Tet)
D = 733 K
Min GSE at a0 = 4.75 Å
CuS (Cubic)
D = 525 K
Min GSE at a0 = 4.5 Å, c/a = 1.12
CuS(Tet)
D = 780 K
CuSe
CuTe
Ground State Energies via Gibbs2: CuSe & CuTe
Min GSE at a0 = 5.0 Å
Cubic
CuSe (Cubic)
D = 409 K
Min GSE at a0 = 5.34 Å
CuTe (Cubic)
D = 327 K
Min GSE at a0 = 4.75 Å, c/a = 1.1
Tetragonal
CuTe (Tet)
D = 622 K
Min GSE at a0 = 5.05 Å, c/a = 1.1
CuTe (Tet)
D = 489 K
Superconductivity and Phonons BCS via Eliashberg-McMillan
† †
, , ,
, ,
( )mn m n
el phH g c c b b
q
k q k k q k q q
k q
,2
2
, , , ,
,
1( ) ( ) ( ) ( )
( )
mn
m F n F
mnF
F gN
q
q k q k k q k
q k
,2
, , , ,
,
2( ) ( )
( )
mn
m F n F
mnF
gN
q
q k q k k q k
kq
2
,0
,
( )2
Fd
q
q
To get , need to compute ,mng
q
k q k!
NB! The “double deltas” will be approximated by two Gaussians
of width “sigma ()” whose numerical convergence is
governed by imposed precision limits and basis set symmetry.
Con Quidado!
Eliashberg-McMillan-Allen-Dynes
, ,
, , ,,
/ 4mn
m KS nh Vg
q
q
q k q kk q k
, ,
,
i
KSKS s
s s
V eV u
u N
q R
q q
R R
D
*
1.04 1exp
1.45 1 0.62CT
Let’s Go!
CuSe TC
D = 409 K; * = 0.0
Cubic
TC(max) ~ 17 K
Tetragonal
TC(max) ~ 36 K
D = 623 K; * = 0.0
CuTe TC
D = 327 K; * = 0.0
Cubic
TC(max) ~ 4.2 K
Tetragonal
TC(max) ~ 45 K
D = 490 K; * = 0.0
CuS TC
D = 525 K; * = 0.0
Cubic
TC(max) ~ 28 K
Tetragonal
D = 780 K; * = 0.0
Whoops! • Unphysically “negative” ! • Convergence issues? • Symmetry issues? • “Needs more work ;-)”
OK...Now What About CuO? Well?
Assume a doping density for“g = 0.15 holes/CuO”
in this region for experimentally
determined Tet-CuO that effectively screens “U” such that we have an “ideal” Fermi liquid.
Then what does Gibbs2 and Eliashberg-McMillan tell us about the possibility of electron-phonon mediated superconducting copper oxide perovskites?
CuO (tetragonal)
q = 0.15/CuO TC
D = 928 K
TC(avg) ~ 75 K
* = 0.05
with maybe a little help from
their spins!
Ipso Facto... At least at optimum
doping...
the holes are paired by lattice
shakes...
So What Else is New? Macfarlane, Rosen, Seki, SSC 63, 831 (1987)
Raman Spectroscopy of YBCO
We can see Phonons have been there
ever since the Creation!
At the End of the Day... Can We Actually Make Any of this Stuff?
Aluminum (Quantum-ESPESSO Example)
* = 0.1 Log_w ~ D
TC(exp) = 1.2 K
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